1. Technical Field
The present invention relates to a position controlling method for a robot, and more particularly, to a position controlling method for a robot in which position control of a horizontal multiple articulation robot or an orthogonal robot is executed at high speed while preventing a residual vibration and preventing unwanted acceleration and deceleration of the robot. These objectives are realized by a discrete time state equation which utilizes a decreased sampling time such that highly precise position control can be executed.
2. Prior Art
Heretofore, various methods have been applied for a position control of a horizontal multiple articulation robot or an orthogonal robot.
Namely, there is a known linear accelerating or decelerating method as shown in FIG. 1. Since this method uses the relation of speed (v) versus time (t), there is discontinuity at points A, B, C, D such that a moving direction of the robot is changed when the robot moves in a trapezoidal waveform around the 0-axis. This method disadvantageously generates a vibration so that the time to decide a movement position of the robot becomes substantially longer.
According to the exponential functional accelerating and decelerating method as shown in FIG. 2, a speed (V(t)) upon acceleration (E) is V(t)=V max {1-exp(t/.tau.)} (.tau.:time constant of the exponential function), a speed (V(Ts)) of a motor at every sampling time (Ts) becomes: V(Ts)=Vmax {1-exp (Ts/.tau.)}, a position (P(Ts)) of the robot at this moment becomes: P(Ts)=V(Ts).times.Ts=Vmax {1 -exp(Ts/.tau.)}.times.Ts . . . (1) and speed (V(t)) of the motor upon deceleration (F) becomes V(t)=Vmax.times.exp (-t/.tau., a speed (V(Ts)) of the motor at every sampling time becomes: V(Ts)=Vmax.times.exp (-Ts/.tau.), and the P(Ts) at this moment becomes: P(Ts)=V(Ts).times.Ts=Vmax.times.exp(-Ts/.tau. . . . (2). Accordingly, a microprocessor can discriminate either the acceleration or deceleration at every sampling time and compute values at every axis by utilizing the aforesaid expressions (1) or (2). Consequently, there have been problems with the sampling time becoming longer, the preciseness of the position path decreasing and the position control system becoming unstable.
Moreover, when there are a plurality of axes (four axes) in the case of a horizontal multiple articulation robot, it is desirable that each axis start simultaneously and terminate at the same time a driving motion is made. In order to prevent a vibration of the robot body generated by an interfering motion at the axis, a speed distribution should be determined by utilizing an amount of movement (Vx(k), Vy(k)) of each axis as shown in FIG. 3, but there have been considerable difficulties accompanying a determination of speed distribution.
U.S. Pat. No. 4,625,285 is a typical example of a conventional robot controller. The patent discloses movement order generating means for instructing a plurality of the movement aiming positions in response to an operating instruction, aiming position variables forming means for compensating a deviation of a plurality of movement aiming positions previously instructed by said movement instruction generating means, a compacting/expanding means for said movement instructing position variable means, aiming position instructing means having a positional instruction adding section for adding an output signal of said plurality of position controlling means so as to output a plurality of instructions compacted or expanded by said compacting/expanding means so as to execute a position control and a speed control upon said movement, and a driving section for outputting a signal for driving the robot according to the aiming position instructions output by said aiming position instructing means, to thereby execute a plurality of the compacting/expanding position processes combined to the output so as to generate a single instruction.
However, since the robot controller includes a very complicated construction as well as complicated controlling processes, not only does it have an increased manufacturing cost, but it also has an aiming position which may be adversely affected. The aiming position is affected because of the addition to the output of each position controlling means. There is also a problem because repair is very difficult when any malfunction of the device occurs.